using a sample of \(n\)  iid observations \(z_i = (y_i,x_i)\) . Examples include non-linear least-squares (NLS) for which \(q(z_i;\theta ) = [y_i - f(x_i;\theta )]^2\)  where \(f\)  is the regression function, known up to the parameters of interest \(\theta \) . For (pseudo) maximum likelihood estimation (MLE), \(q(z_i;\theta ) = -\ell (y_i;\theta |x_i)\)  is the negative of the log-likelihood. The true value, denoted by \(\theta ^\dagger \) , minimizes the limiting objective \(Q = \text{plim}_{n\rightarrow \infty } Q_n\) .
Under the conditions in Theorem 2.1 of [1]}, \(\hat{\theta }_n\)  is consistent for \(\theta ^\dagger \) . If, in addition, the assumptions in Theorem 3.1 of [1]} hold, then \(\hat{\theta }_n\)  is also asymptotically normal:
\(\sqrt{n}V_n^{-1/2}(\hat{\theta }_n-\theta ^\dagger )\overset{d}{\rightarrow } N(0,I_d), \) 
